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Learn the Knight's Tour (Basic)

The Knight's Tour

The Knight's Tour is a famous chess puzzle. The object is to move the Knight around the board using only valid L-shaped Knight moves, so that each square is visited exactly once

Solving the puzzle may seem impossible (Try it yourself) but by following a few simple rules you will soon learn how to complete the tour speedily and with ease. Your friends will be amazed at your mental powers!

Once you have mastered the basic tour, you can then learn how to solve the Advanced Challenge in which both starting and end squares are chosen at the beginning.

Learning the Basic Knight's Tour

Quadrants and Systems

First you have to familiarise yourself with the Four Quadrants of the chess board, and with the Four Systems of moves.

The Four Quadrants are shown here using different colors for each quadrant.

The Four Quadrants

The Four Systems are sequences of moves that form a pattern. The moves in each system can be considered separately from those of the other systems. This makes completing the Knight's Tour simply a matter of completing the moves in one system before moving on to the next.

There are two diamond-shaped systems and two square-shaped systems. The shape is repeated in each quadrant, collectively forming all the moves for that particular system.

For each shape (diamond or square) there are two orientations, a left-hand shape and a right-hand shape.

The left-hand diamonds point up to the left, whereas the right-hand diamonds point up to the right.

The left-hand square has the topmost square on the left side of the quadrant, whereas the right-hand square has the topmost square on the right side of the quadrant.

The Four Systems are shown in the following illustrations.

Left-Hand Diamond System

Right-Hand Diamond System

Left-Hand Square System

Right-Hand Square System

How to Complete the Basic Knight's Tour

Once you understand the quadrants and systems, completing the Knight's Tour is child's play.

First, you simply note which system the Knight occupies on its opening move. Then move the Knight around the other three squares of this system within the same quadrant before moving on to do the same in the next quadrant.

All you have to worry about is that the final move in each quadrant allows you to move on to the same system in the another quadrant. To do this, you need to decide whether to move clockwise or anti-clockwise around each quadrant so that you don't get trapped on your final move. As long as you make sure that your final move in each quadrant is as near the center of the board as possible, you will be OK.

When you move into the final quadrant of the system, you must choose your direction of movement carefully to ensure that the final move in that quadrant allows you to move on to another system. You then simply repeat this procedure through the second system, before moving on to the third and finally the fourth system, until you have fully completed the Knight's Tour!

You should note that the four systems are completed in a particular sequence. A diamond-shaped system must be followed by one of the square-shaped systems, and vice versa.